Problem: Simplify the following expression: $ q = -10 + \dfrac{-x}{x - 4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{x - 4}{x - 4}$ $ \dfrac{-10}{1} \times \dfrac{x - 4}{x - 4} = \dfrac{-10x + 40}{x - 4} $ Therefore $ q = \dfrac{-10x + 40}{x - 4} + \dfrac{-x}{x - 4} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-10x + 40 - x}{x - 4} $ $q = \dfrac{-11x + 40}{x - 4}$